大尺寸直拉硅单晶生长的多物理场建模与优化

doi:10.16553/j.cnki.issn1000-985x.20241022.001

摘要/Abstract

摘要： 随着光伏和半导体行业的快速发展,制备更大直径(12英寸及以上,1英寸=2.54 cm)的硅单晶成为趋势,直拉法作为硅单晶最主要的制备方法备受重视。然而在制备大直径和高质量的直拉硅单晶的过程中,随着晶体直径和坩埚尺寸的增加,熔体体积显著增加,热场、流场及应力场的复杂性显著提升,涡流、热浮力和科里奥利力的相互作用会造成熔体流动的强烈湍流和速度、温度波动,出现诸如固液界面温度分布不均,熔体内热对流复杂等问题,从而影响硅单晶中的缺陷分布。因此,如何实现对工艺参数的控制,以获得理想的大直径硅晶体具有重要的研究意义。本文针对实际生产的滞后性和成本问题,建立了可以实时预测、动态控制和优化工艺参数的40英寸热场制备18英寸硅单晶棒的二维轴对称全局数值模拟模型,考虑了坩埚深度及热传导路径的延长,在主加热器的基础上,增加底部加热器,采用有限元法逐一分析晶体转速、坩埚转速、气体压强的变化对单晶硅热场和硅晶体生长的影响,包括固液界面形状、温度梯度、V/G值、氧浓度及缺陷分布等。通过多次仿真实验,获得了一组较为合适的工艺参数组合:晶体转速15 r/min、坩埚转速5 r/min、炉内气压1 200 Pa,可使固液界面温度梯度较小,且温度分布更加均匀,有效避免了过度湍流化。进一步采用制备18英寸硅单晶棒的验证实验及性能检测发现,采用仿真所得最优工艺参数组合生产的硅单晶棒能将成晶率提升至87.44%。这组针对18英寸硅单晶棒的最佳工艺参数组合(包括晶体转速、坩埚转速及炉内气压等)经过精细优化,主要基于大尺寸(12英寸及以上)直拉硅单晶生长过程中热场和流场的复杂性,对大尺寸硅单晶具有较好的适应性,但在更小尺寸(如4、6或8英寸)的硅单晶生长中,由于热传递和气流扰动的不同,最佳工艺参数组合可以作为参考,但还需要进行具体条件下的验证和调整。本研究建立的数字化模型能够准确预测并优化大尺寸直拉硅单晶的生长过程,提质降本,具有实际应用前景。

关键词: 硅单晶, 直拉法, 二维轴对称, 有限元法, 工艺参数, 数值模拟, 数字化模型

Abstract: With the rapid advancement of the photovoltaic and semiconductor industries, the trend towards producing larger diameter (12 inch and above, 1 inch=2.54 cm) silicon single crystal has become increasingly prominent. The Czochralski method, as a predominant technique for silicon single crystal production, is highly emphasized. However, during the growth of large-diameter, high-quality Czochralski silicon single crystals, the enlargement in both crystal diameter and crucible size significantly expands the melt volume, thereby intensifying the complexity of the thermal field, flow field, and stress field. The interaction between vortices, thermal buoyancy, and Coriolis forces induces substantial turbulence and causes fluctuations in the melt's flow velocity and temperature, leading to challenges such as uneven temperature distribution at the solid-liquid interface and complex thermal convection within the melt, which can impact the defect distribution within the silicon crystals. Therefore, how to control process parameters to achieve ideal silicon single crystals with large-diameter is of significant importance. This study established a two-dimensional axisymmetric global numerical simulation model for the preparation of 18-inch crystal silicon rods within a 40-inch thermal field, capable of real-time prediction, dynamic control, and optimization of process parameters to address delays and cost issues in actual production. The model takes into account the increased crucible depth and extended heat conduction path, and incorporates an additional bottom heater alongside the main heater. Using the finite element method, the effects of variations in crystal rotation speed, crucible rotation speed, and gas pressure on the thermal field and silicon single crystal growth were analyzed individually, including shape of solid-liquid interfaces, temperature gradient, value of V/G, oxygen concentration and defect distribution, etc. Through multiple simulation experiments, a set of optimal process parameters was identified: a crystal rotation speed of 15 r/min, a crucible rotation speed of 5 r/min, and a furnace gas pressure of 1 200 Pa, which can make the temperature gradient of solid-liquid interface smaller and the temperature distribution more uniform, effectively avoiding excessive turbulence. Crystal growth experiments and a series of tests show that thesilicon single crystal rods produced with the optimal process parameters obtained from the simulation can increase the crystallization rate to 87.44%. This set of optimal process parameters for the 18-inch silicon single crystal rods (including crystal rotation speed, crucible rotation speed, and furnace pressure) has been precisely optimized based on the complexities of the thermal and flow fields in the growth of large-diameter (12 inches and above) Czochralski silicon single crystals. These parameters are well-suited for large-diameter silicon single crystal growth but may require specific adjustments and validation for smaller diameters (such as 4, 6 or 8-inch), where differences in heat transfer and airflow disturbances must be taken into account. The digital model established in this study can accurately predict and optimize the growth process of large-size Czochralski silicon single crystal, and have practical application prospects.

Key words: silicon single crystal, Czochralski method, two-dimensional axisymmetriy, finite element method, process parameter, numerical simulation, digital model

中图分类号:

O782⁺.5

林海鑫, 高德东, 王珊, 张振忠, 安燕, 张文永. 大尺寸直拉硅单晶生长的多物理场建模与优化[J]. 人工晶体学报, 2025, 54(1): 17-33.

LIN Haixin, GAO Dedong, WANG Shan, ZHANG Zhenzhong, AN Yan, ZHANG Wenyong. Multi-Physics Field Modeling and Optimization of Large-Size Czochralski Silicon Single Crystal Growth[J]. Journal of Synthetic Crystals, 2025, 54(1): 17-33.

参考文献

[1] LI Z X, SMIRNOV A. Application of computer modeling to pulling rate and productivity of Czochralski pullers in PV Si crystal growth[J]. Journal of Crystal Growth, 2023, 611: 127178.
[2] BORISOV D V, KALAEV V V. ILES of melt turbulent convection with conjugated heat transfer in the crucible and gas flow for Czochralski silicon crystal growth system[J]. Journal of Crystal Growth, 2021, 573: 126305
[3] WANG Z X, REN Y S, MA W H, et al. Crystal surface heat transfer during the growth of 300 mm monocrystalline silicon by the Czochralski process[J]. International Journal of Heat and Mass Transfer, 2025, 236: 126259.
[4] LI Y, GAO M M, LI J, et al. Effect of gas flow rate on chemical reactions in Czochralski silicon crystal growth[J]. Journal of Crystal Growth, 2018, 504: 56-61.
[5] MACHIDA N, HOSHIKAWA K, SHIMIZU Y. The effects of argon gas flow rate and furnace pressure on oxygen concentration in Czochralski silicon single crystals grown in a transverse magnetic field[J]. Journal of Crystal Growth, 2000, 210(4): 532-540.
[6] 高宇, 朱亮, 张俊, 等. 定拉速生长对ϕ300 mm直拉硅单晶生长影响分析[J]. 人工晶体学报, 2020, 49(5): 811-814+823. GAO Y, ZHU L, ZHANG J, et al. Analysis of ϕ300 mm CZ silicon single crystal growth with constant growth rate[J]. Journal of Synthetic Crystals, 2020, 49(5): 811-814+823 (in Chinese).
[7] JEON H J, PARK H, KOYYADA G, et al. Optimal cooling system design for increasing the crystal growth rate of single-crystal silicon ingots in the Czochralski process using the crystal growth simulation[J]. Processes, 2020, 8(9): 1077.
[8] 徐尊豪, 李进, 何显, 等. 高拉速对ϕ300 mm单晶硅点缺陷分布及生产能耗的影响[J]. 人工晶体学报, 2023, 52(4): 562-570. XU Z H, LI J, HE X, et al. Effect of high pulling rate on the distribution of point defects and energy consumption in ϕ300 mm monocrystalline silicon[J]. Journal of Synthetic Crystals, 2023, 52(4): 562-570 (in Chinese).
[9] LOU Z S, XUE Z X, YUAN S, et al. Effects of horizontal magnetic field position on oxygen control in 12-inch Czochralski silicon[J]. Journal of Crystal Growth, 2024, 646: 127861.
[10] NOGHABI O A, JOMÂA M, M'HAMDI M. Analysis of W-shape melt/crystal interface formation in Czochralski silicon crystal growth[J]. Journal of Crystal Growth, 2013, 362: 77-82.
[11] PÄTZOLD O, DADZIS K, KIRMSE C, et al. Model experiments for melt flow in Czochralski growth of silicon[J]. Journal of Crystal Growth, 2022, 588: 126656.
[12] ASADI NOGHABI O, M'HAMDI M, JOMÂA M. Effect of crystal and crucible rotations on the interface shape of Czochralski grown silicon single crystals[J]. Journal of Crystal Growth, 2011, 318(1): 173-177.
[13] SABANSKIS A, PLĀTE M, SATTLER A, et al. Evaluation of the performance of published point defect parameter sets in cone and body phase of a 300 mm Czochralski silicon crystal[J]. Crystals, 2021, 11(5): 460.
[14] LIU X, HARADA H, MIYAMURA Y, et al. Transient global modeling for the pulling process of Czochralski silicon crystal growth. II. Investigation on segregation of oxygen and carbon[J]. Journal of Crystal Growth, 2020, 532: 125404.
[15] LIU Y Y, LIU D, SONG Z Z. Simulation study on control characteristics of semiconductor grade monocrystalline silicon growth process[C]//2022 China Automation Congress (CAC). November 25-27, 2022, Xiamen, China. IEEE, 2022: 5075-5080.
[16] 张晶, 刘丁. ϕ300 mm 直拉硅单晶生长过程中的变晶现象及其影响因素[J]. 人工晶体学报, 2022, 51(7): 1185-1193.
ZHANG J, LIU D. Transformation phenomena and influencing factors in the growth process of ϕ300 mm Czochralski silicon single crystal[J]. Journal of Synthetic Crystals, 2022, 51(7): 1185-1193 (in Chinese).
[17] GUSEV A O, MAZHOROVA O S. Quasi-steady-state numerical simulation of Czochralski single crystal growth[J]. Keldysh Institute Preprints, 2023(59): 1-20.
[18] MUKAIYAMA Y, SUEOKA K, MAEDA S, et al. Numerical analysis of effect of thermal stress depending on pulling rate on behavior of intrinsic point defects in large-diameter Si crystal grown by Czochralski method[J]. Journal of Crystal Growth, 2020, 531: 125334.
[19] KUTSUKAKE K, NAGAI Y, BANBA H. Virtual experiments of Czochralski growth of silicon using machine learning: influence of processing parameters on interstitial oxygen concentration[J]. Journal of Crystal Growth, 2022, 584: 126580.
[20] SU J Y, ZHANG X Y, LI X, et al. Synthesis and luminescence properties of Yb³⁺, Tm³⁺ and Ho³⁺ co-doped SrGd₂(WO₄)₂(MoO₄)₂ nano-crystal[J]. Advanced Powder Technology, 2020, 31(3): 1051-1059.
[21] DJEUMEGNI J, LAZARD M, DEZ V, et al. Modeling of radiative heat transfer in a gray semi-transparent medium with internal fluid cavity limited by black boundary surfaces[J]. Tecnica Italiana-Italian Journal of Engineering Science, 2019, 63(2/3/4): 205-210.
[22] MCMULLEN R M, KRYGIER M C, TORCZYNSKI J R, et al. Navier-stokes equations do not describe the smallest scales of turbulence in gases[J]. Physical Review Letters, 2022, 128(11): 114501.
[23] MORI A, SATO M, SUZUKI Y. Effect of density change at crystallization on a one-dimensional heat balance equation at solid-liquid interface[J]. Japanese Journal of Applied Physics, 2019, 58(4): 045506.
[24] PENG J Z, LIU X L, AUBRY N, et al. Data-driven modeling of geometry-adaptive steady heat transfer based on convolutional neural networks: heat conduction[EB/OL]. 2020: 2010.03854[2024-06-30]. https://arxiv.org/abs/2010.03854v1.
[25] WU H H, GAO D D, WANG S, et al. Design of follow-up superconducting Cusp magnetic field and system performance analysis of Czochralski single crystal furnace[J]. Results in Physics, 2023, 53: 106958.
[26] SUEZAWA M, YONENAGA I. Modification of the critical v/G of the Voronkov's theory on the grown-in defects in Si crystals[J]. Japanese Journal of Applied Physics, 2020, 59(9): 098001.
[27] MUKAIYAMA Y, SUEOKA K, MAEDA S, et al. Unsteady numerical simulations considering effects of thermal stress and heavy doping on the behavior of intrinsic point defects in large-diameter Si crystal growing by Czochralski method[J]. Journal of Crystal Growth, 2020, 532: 125433.